Confluence for Proof-Nets via Parallel Cut Elimination

Giulio Guerrieri; Giulia Manara; Lorenzo Tortora de Falco; Lionel Vaux Auclair

doi:10.29007/vkfn

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Confluence for Proof-Nets via Parallel Cut Elimination

20 pages•Published: May 26, 2024

Giulio Guerrieri, Giulia Manara, Lorenzo Tortora de Falco and Lionel Vaux Auclair

Abstract

We provide the first proof of confluence for cut elimination in multiplicative-exponential linear logic proof-nets that is not based on Newman’s lemma or strong normalization, not even indirectly. To achieve our goal, we take inspiration from Tait and Martin-Lof’s method based on parallel reduction for the lambda-calculus, even though the wilder realm of untyped proof-nets makes the proof subtler and more challenging.

Keyphrases: confluence, cut elimination, hypergraphs, linear logic, parallel reduction, proof-net

In: Nikolaj Bjorner, Marijn Heule and Andrei Voronkov (editors). Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 100, pages 464--483

Links:	https://easychair.org/publications/paper/kGr4
	https://doi.org/10.29007/vkfn

BibTeX entry

@inproceedings{LPAR2024:Confluence_for_Proof_Nets_via,
  author    = {Giulio Guerrieri and Giulia Manara and Lorenzo Tortora de Falco and Lionel Vaux Auclair},
  title     = {Confluence for Proof-Nets via Parallel Cut Elimination},
  booktitle = {Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Nikolaj Bj\{\textbackslash{}o\}rner and Marijn Heule and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {100},
  pages     = {464--483},
  year      = {2024},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/kGr4},
  doi       = {10.29007/vkfn}}

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